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7. MOTION
hard
An object starting from rest travels $20\, m$ in first $2\,\sec $ and $160\, m$ in next $4\,\sec $. What will be the velocity after $7\,\sec $ from the start ?
A
$0.07 \,ms ^{-1}$
B
$700 \,ms ^{-1}$
C
$0.7 \,ms ^{-1}$
D
$70 \,ms ^{-1}$
Solution
$s_{1}=u t+\frac{1}{2} a t^{2}$ or $20=0+\frac{1}{2} a(2)^{2}$ or $a=10 \,ms ^{-1}$
$v=u+a t=0+(10 \times 2)=20\, ms ^{-1}$
$s_{2}=160=u t^{\prime}+\frac{1}{2} a^{\prime}\left(t^{\prime}\right)^{2}=(20 \times 4)+\left(\frac{1}{2} a^{\prime} \times 16\right) \Rightarrow a^{\prime}=10 \,ms ^{-2}$
since acceleration is the same, we have $v'=0+(10 \times 7)=70 \,ms ^{-1}$
Standard 9
Science
